arXiv research

The world GDP distribution is described using thermodynamics principles.

The paper develops efficient algorithms for sampling from random spanning trees and determinantal point processes.

The study applies wealth thermalization hypothesis to social networks and explains inequality.

The paper analyzes the excess risk of PCA and provides a precise characterization.

In this note we consider sampling from (non-homogeneous) strongly Rayleigh probability measures. As an important corollary, we obtain a fast mixing Markov Chain sampler for Determinantal Point Processes.

Affirm Lord Rayleigh's conjecture on curved spaces for clamped plates.

In this paper we derive estimates to the free boundary problem for the Euler equation with surface tension, and without surface tension provided the Rayleigh-Taylor sign condition holds. We prove that as the surface tension tends to zero, when the Rayleigh-Taylor condition is satisfied, solutions converge to the Euler …

Generalized R2R handles non-Gaussian noise for deep network training.

Physics-informed neural networks improve surrogate modeling of turbulent Rayleigh-Bénard convection.

The paper proves instability of translating λ-solitons and provides bounds on their length.

The paper derives the QGS equations using stochastic central extensions.

We consider the SO(3) Witten-Reshetikhin-Turaev quantum invariants of random 3-manifolds. When the level r is prime, we show that the asymptotic distribution of the absolute value of these invariants is given by the standard Rayleigh distribution and independent of the choice of level. Hence the probability that the qu…

Paper develops IFTRR to solve sparse generalized eigenvalue problems efficiently.

New criterion for cylinder stability in curved spaces.

Strongly log-concave (SLC) distributions are a rich class of discrete probability distributions over subsets of some ground set. They are strictly more general than strongly Rayleigh (SR) distributions such as the well-known determinantal point process. While SR distributions offer elegant models of diversity, they lac…

New method estimates sparse canonical vectors efficiently.

We introduce in this paper a new algorithm for Multi-Armed Bandit (MAB) problems. A machine learning paradigm popular within Cognitive Network related topics (e.g., Spectrum Sensing and Allocation). We focus on the case where the rewards are exponentially distributed, which is common when dealing with Rayleigh fading c…

Improved lower bound for first eigenvalue of minimal hypersurfaces in spheres.

Physics-informed model reduces RBC simulation costs.

We study probability measures induced by set functions with constraints. Such measures arise in a variety of real-world settings, where prior knowledge, resource limitations, or other pragmatic considerations impose constraints. We consider the task of rapidly sampling from such constrained measures, and develop fast M…

Study on GEPs with generative priors, showing optimal statistical rates and proposing an iterative algorithm.

A thermodynamic theory explains EU election vote distributions.

Proposes a framework to extract ordered eigenfunctions from contextual kernels.

Recent work has shown deep learning can accelerate the prediction of physical dynamics relative to numerical solvers. However, limited physical accuracy and an inability to generalize under distributional shift limit its applicability to the real world. We propose to improve accuracy and generalization by incorporating…

We consider a column of a rotating stationary surface in Euclidean space. We obtain a value $l_0>0$ in such way that if the length $l$ of column satisfies $l>l_0$, then the surface is instable. This extends, in some sense, previous results due to Plateau and Rayleigh for columns of surfaces with constant mean curvature…

Study stability and bifurcation of liquid interfaces in cylindrical supports.

This note proves a Gaussian version of a Pólya-Szegö conjecture using rearrangement techniques.

Channel modeling is a critical topic when considering designing, learning, or evaluating the performance of any communications system. Most prior work in designing or learning new modulation schemes has focused on using highly simplified analytic channel models such as additive white Gaussian noise (AWGN), Rayleigh fad…

New scheme optimizes BMI through probabilistic and geometric shaping.

For a bounded domain $Ω$ with a piecewise smooth boundary in a complete Riemannian manifold $M$, we study eigenvalues of the Dirichlet eigenvalue problem of the Laplacian. By making use of a fact that eigenfunctions form an orthonormal basis of $L^2(Ω)$ in place of the Rayleigh-Ritz formula, we obtain inequalities for …

Sparse generalized eigenvalue problem (GEP) plays a pivotal role in a large family of high-dimensional statistical models, including sparse Fisher's discriminant analysis, canonical correlation analysis, and sufficient dimension reduction. Sparse GEP involves solving a non-convex optimization problem. Most existing met…

The paper extends a spectral evolution model for link prediction in evolving networks.

The techniques and analysis presented in this paper provide new methods to solve optimization problems posed on Riemannian manifolds. A new point of view is offered for the solution of constrained optimization problems. Some classical optimization techniques on Euclidean space are generalized to Riemannian manifolds. S…

Enhanced VMC methods improve neural wavefunction training.

Study chaotic dynamics in social stratification models leading to thermalization and turbulence.

Paper introduces REED for noncoherent OTA-FL, reducing latency without phase alignment.

This article proposes and evaluates a technique to predict the level of interference in wireless networks. We design a recursive predictor that estimates future interference values by filtering measured interference at a given location. The predictor's parameterization is done offline by translating the autocorrelation…

New MIMO constellation design for noncoherent communications reduces hardware complexity.

Sharp-SSL uses random projections to identify important variables for semi-supervised learning.

We study dual volume sampling, a method for selecting k columns from an n x m short and wide matrix (n <= k <= m) such that the probability of selection is proportional to the volume spanned by the rows of the induced submatrix. This method was proposed by Avron and Boutsidis (2013), who showed it to be a promising met…

We produce a new proof and extend results by Harrell and Stubbe for the discrete spectrum of a self-adjoint operator. An abstract approach--based on commutator algebra, the Rayleigh-Ritz principle, and an ``optimal'' usage of the Cauchy-Schwarz inequality--is used to produce ``parameter-free'', ``projection-free'' vers…

We discuss two generalizations of the inverse problem of the calculus of variations, one in which a given mechanical system can be brought into the form of Lagrangian equations with non-conservative forces of a generalized Rayleigh dissipation type, the other leading to Lagrangian equations with so-called gyroscopic fo…

In this paper we formulate a geometric theory of the mechanics of growing solids. Bulk growth is modeled by a material manifold with an evolving metric. Time dependence of metric represents the evolution of the stress-free (natural) configuration of the body in response to changes in mass density and "shape". We show t…

In this note, we investigate upper bounds of the Neumann eigenvalue problem for the Laplacian of a bounded domain (with smooth boundary) in a given complete (not compact a priori) Riemannian manifold with Ricci bounded below . For this, we use test functions for the Rayleigh quotient subordinated to a family of open se…

New algorithm approximates maximum of certain distributions on subsets.

We establish a link between Fourier optics and a recent construction from the machine learning community termed the kernel mean map. Using the Fraunhofer approximation, it identifies the kernel with the squared Fourier transform of the aperture. This allows us to use results about the invertibility of the kernel mean m…

We study Lord Rayleigh's problem for clamped plates on an arbitrary $n$-dimensional $(n\geq 2)$ Cartan-Hadamard manifold $(M,g)$ with sectional curvature $\textbf{K}\leq -κ^2$ for some $κ\geq 0.$ We first prove a McKean-type spectral gap estimate, i.e. the fundamental tone of any domain in $(M,g)$ is universally bounde…

The idea of end-to-end learning of communications systems through neural network -based autoencoders has the shortcoming that it requires a differentiable channel model. We present in this paper a novel learning algorithm which alleviates this problem. The algorithm iterates between supervised training of the receiver …